Forecasting the future: is it possible for adiabatically time-varying nonlinear dynamical systems?

Rui Yang*, Ying-Cheng Lai, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Nonlinear dynamical systems in reality are often under environmental influences that are time-dependent. To assess whether such a system can perform as desired or as designed and is sustainable requires forecasting its future states and attractors based solely on time series. We propose a viable solution to this challenging problem by resorting to the compressive-sensing paradigm. In particular, we demonstrate that, for a dynamical system whose equations are unknown, a series expansion in both dynamical and time variables allows the forecasting problem to be formulated and solved in the framework of compressive sensing using only a few measurements. We expect our method to be useful in addressing issues of significant current concern such as the sustainability of various natural and man-made systems. (C) 2012 American Institute of Physics.

Original languageEnglish
Article number033119
Number of pages6
JournalChaos
Volume22
Issue number3
Early online date2 Aug 2012
DOIs
Publication statusPublished - Sep 2012

Keywords

  • chaos
  • equation
  • series
  • prediction
  • reconstruction

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